Signal types

Signals that are (or are indistinguishable) from filtered (coloured) white noise

Transients

Whatever does't fit above I guess

Signal analysis

Sinusoidal

Good when most of the energy is contained in a few sinusoids. May be problematic for very harmonic signals, e.g. a male voice may have close to a hundred harmonics in the full audio band.

Pitch

Good for harmonic signals. Hard to estimate and code when extra sinusoids and noise are present. At 48 kHz, no need for fractional pitch or anything like that, but sub-band pitch analysis or multi-tap gain is a good idea. Also, there needs to be a way to remove the effect of sinusoids and noise. Even then removing the "noise" also means removing all excitation to the pitch predictor, so that's a problem.

MDCT

Very general. Can code anything, but not very good at anything. High delay (2x frame size). Could put several "MDCT frames" in each codec frame to make latency smaller.

Wavelets

Just a fancy name for sub-bands with non-uniform width. Probably similar to having an MDCT with few sub-bands, except that that the sub-bands could follow (roughly) the critical bands.

LPC + stochastic cb

Like CELP with no pitch. Could be used to code the noisy part of the signal with low bit-rate. Would need to figure out how to preserve the energy of the noise when going with 1/2 bit per sample and less.

Codec Structure Ideas

Sinusoidal + wavelet

Preemphasis

Extract as many sinusoids as possible

Wavelet transform

Code wavelet coefs using VQ

Sinusoidal, pitch and noise

Preemphasis

Joint pitch + sinusoidal estimation

LPC analysis

CELP-like coding of the residual (mainly noise)

Estimation Ideas

Sinusoid Estimation

Very hard to do properly, especially with reasonable complexity and low delay. Some ideas:

Least-square type matching

Step one: estimate sinusoid frequencies.

Tried so far:

MUSIC fails on non-trivial signals and very complex, although there's an AES paper that recommends first whitening the noise part of the signal before applying the algo. Haven't tried that so far.

ESPRIT fails on non-trivial signals and very complex (see above for possible solution)

LPC would probably work, but requires an insane order -> impractical, plus it tends to be numerically unstable anyway.

FFT poor resolution, but that's all we have left so far. There's an AES paper that describes a sort of time-domain phase unwrapping that could help.

Step two: what to match

Step three: solving

Looks like it's possible to solve an NxM least square problem in O(N*M) time using an iterative algorithm as long as the system matrix is near-orthogonal. If we want to solve Ax=b and A^h*A ~= I, then we start with x(0)=A^h*b and then: